Cook the noodles according to package directions until just tender. Drain them well and set aside.
Heat the vegetable oil in a large wok or skillet over medium-high heat.
Add the sliced chicken and cook until browned and cooked through, about 5 to 7 minutes. Remove the chicken from the wok and set it aside.
Add the garlic, broccoli, carrots, and onion to the wok. Stir-fry for 3 to 4 minutes until the vegetables are crisp-tender.
In a small bowl, whisk together the soy sauce, oyster sauce, sesame oil, white pepper, and chicken broth to create the sauce.
Return the cooked chicken to the wok. Add the cooked noodles.
Pour the sauce mixture over the noodles and chicken. Toss everything together quickly for 1 to 2 minutes until the noodles are evenly coated and heated through.
Serve immediately, garnished with chopped green onions.
Notes
For a vegetarian version, substitute the chicken with 8 ounces of firm tofu, pressed and cubed.
If you do not have oyster sauce, you can substitute it with an equal amount of vegetarian stir-fry sauce or more soy sauce mixed with a pinch of sugar.
Cook the noodles slightly less than the package suggests, as they will continue to cook when stir-fried.